Question: Solve for $a$, $ -\dfrac{7}{10a + 10} = \dfrac{5}{2a + 2} + \dfrac{3a - 1}{2a + 2} $
Answer: First we need to find a common denominator for all the expressions. This means finding the least common multiple of $10a + 10$ $2a + 2$ and $2a + 2$ The common denominator is $10a + 10$ The denominator of the first term is already $10a + 10$ , so we don't need to change it. To get $10a + 10$ in the denominator of the second term, multiply it by $\frac{5}{5}$ $ \dfrac{5}{2a + 2} \times \dfrac{5}{5} = \dfrac{25}{10a + 10} $ To get $10a + 10$ in the denominator of the third term, multiply it by $\frac{5}{5}$ $ \dfrac{3a - 1}{2a + 2} \times \dfrac{5}{5} = \dfrac{15a - 5}{10a + 10} $ This give us: $ -\dfrac{7}{10a + 10} = \dfrac{25}{10a + 10} + \dfrac{15a - 5}{10a + 10} $ If we multiply both sides of the equation by $10a + 10$ , we get: $ -7 = 25 + 15a - 5$ $ -7 = 15a + 20$ $ -27 = 15a $ $ a = -\dfrac{9}{5}$